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Demography

…or, why is foaling by 2-year-olds not more common.

(image source: http://www.thehorse.com)

Young, still growing, mares face greater challenges to succesfully foaling (image source: http://www.thehorse.com)

Our transition from child to adult is a fraught with physical and mental challenges, made worse by our inexperience. We are less able, when our life’s challenges are greatest. Its tough being a teen.

For horses the transition to adulthood occurs from about just before their first birthday through their second year and, for some, into the beginning of their 3rd year. Compared to people, horses (and most other animals), mature quickly.

A demanding, vulnerable time

Young mares are naive and still investing into growing their bodies. Their inexperience at competing for resources, like food and shelter, and protecting themselves from risks, like aggressors, competitors and predators, makes them vulnerable.

They have not yet formed protective relationships with other mares [1] and a stallion [2] in a breeding and social group called a band. They will, at some time during their teens and probably around their first oestrus, leave their mothers band for another – called natal dispersal [3].

During their teens they may move often between bands – called social dispersal [3] – where they will be more attacked and harassed by other mares, stallions, and bachelor males than at any other time in their lives. It is a high-risk period and the consequence is reproductive failure.

Reproductive delay

The challenges of maturing and growing can delay a mares first foaling and makes rates of reproductive failure higher in younger mares such that foaling rates rise as mares age into their middle years.

Mares are capable of conceiving as soon as they reach sexual maturity around 1 year and, therefore, foaling as a 2-year-old but more commonly they will foal for the first time as 3-, 4-, or 5-year-olds because the physical, cognitive (mental), and social demands of maturing place great demands on them.

Young mare foaling rates measured

The age that mares first breed and foaling rates of young mares have been measured in only a handful of studies where frequent observations have meant that mare birth dates were known and their subsequent foals found.

On Assateague Island National Seashore no 2-year-olds foaled but 23% of 3-year-olds did and from there foaling rates increased up to 69% in 6-year-olds [4]. Similar values with mare age are reported from Nevada, and Cumberland Island, Georgia [5, 6] (see accompanying graphic).

young mare foalingStallions impact on young mare breeding?

The pattern of climbing foaling success was very different in the Pryor Mountain population [7] because, although 2-year-olds did not foal and older mares had comparative low foaling rate, 3-year-olds had a substantial foaling rate – almost identical to the extraordinary foaling rate of 3-year-olds in Joel Berger’s erupting population in the Granite Range, Nevada [8].

I suspect that this difference reflects the extremely mare-biased adult sex ratio due to stallion removals from that population. Where there are substantially fewer stallions, the costs of social dispersal and sexual harassment for 1- and 2-year-old mares breeding for the first time might be substantially reduced. Sexual and social competition have consequences, especially during dispersal for first-time breeders.

Teen pregnancy in Nevada

The magnitude of the eruptive reproductive rates that Joel Berger observed in the Granite Range, Nevada (1979-93) are best revealed when plotted for comparison against other populations [8]. Not only were 2 year olds foaling, but all mares 2 years old and older were foaling at the highest rates ever reported. A remarkable 86% of mares foaled in their sixth year.

The extraordinary foaling rates are because a suite of historical events, particularly the removal of cattle – a competitor of horses – combined to improve the amount and quality of food (grass) available to the Granite Range population.

Kaimanawa mare foaling unremarkable

Although many claimed that Kaimanawa population was undergoing eruptive growth like the populations described in the Granite Range, and Jackie’s and Beaty’s Butte, Oregon, the data on foaling rates by mares did not support those claims [9].

The graphic serves to show how unremarkable foaling rates by young mares in the Kaimanawa Ranges were compared to other populations. Foaling rates by 3 and 4-year-olds were year olds were low compared to all except the Cumberland Island population, Georgia [6].

Interestingly though, in 1998 a single two-year-old foaled – the first and only one to do so. Was this an indication of improved range conditions because musters had reduced horse densities?

Bibliography

1. Cameron, E. Z., Setsaas, T. & Linklater, W. L. Social bonds between unrelated females increase reproductive success in feral horses. Proceedings of the National Academy of Sciences of the United States of America 106, 13850-13853 (2009).

2. Linklater, W. L., Cameron, E. Z., Minot, E. O. & Stafford, K. J. Stallion harassment and the mating system of horses. Animal Behaviour 58, 295-306 (1999).

3. Linklater, W. & Cameron, E. Social dispersal but with philopatry reveals incest avoidance in a polygynous ungulate. Animal Behaviour 77, 1085-1093 (2009).

4. Keiper, R. & Houpt, K. Reproduction in feral horses: An eight year study. American Journal of Veterinary Research 45, 991-995 (1984).

5. Siniff, D. B., Tester, J. R. & McMahon, G. L. Foaling rate and survival of feral horses in Western Nevada. Journal of Range Management 39, 296-297 (1986).

6. Goodloe, R. B., Warren, R. J., Osborn, D. A. & Hall, C. Population characteristics of feral horses on Cumberland Island, Goergia and their management implications. Journal of Wildlife Management 64, 114-121 (2000).

7. Garrott, R. & Taylor, L. Dynamics of a feral horse population in Montana. Journal of Wildlife Management 54, 603-612 (1990).

8. Berger, J. Wild horses of the Great Basin. (University of Chicago Press, 1986).

9. Linklater, W. L., Cameron, E. Z., Minot, E. O. & Stafford, K. J. Feral horse demography and population growth in the Kaimanawa Ranges, New Zealand. Wildlife Research 31, 119-128 (2004).

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For many years during the early, vigorous debates about how fast wild horse populations could grow, the ability of younger mares to foal, especially 2-year-olds, was unknown. The first few studies found that 2-year-olds did not foal and so it was believed unlikely.

Even in the Chincoteague Ntional Seashore, a population with comparatively high reproductive rates at ? foals for every other horse, 2-year-olds were not reported to foal (image source: )

Even on the Chincoteague Island, a population in which mare foaling rates were the highest reported (74% during 1975-82), 2-year-olds were not reported to foal (image source: http://a-glo.com/Wildlife/wildlife51.htm).

The first few studies of wild horse demography, by Ronald Keiper on Assateague Island (1975-79) [1] and Lee Boyd from Wyoming’s Red Desert (1978-79) [2], found no 2-year-olds foaled.

Even in populations like Chincoteague (1975-82), with the highest foaling rates reported, no 2-year-old mares foaled.

Pregnancy testing wild mares

The early development of pregnancy testing by radioimmunoassay and its application to wild mares mustered from their range also found no evidence for 2-year-old foaling.

From three places near Salmon, Idaho, during October, 1980, musters removed about half the horses – 300 horses all together including 137 mares – but found no evidence of pregnancy in 1-year-olds or lactation by 2-year-olds [3].

Mares most often foal for the first time as 3- or 4-year-olds and some older still, having become pregnant as 2-year-olds. Nevertheless, yearlings can also successfully conceive and foal s 2-year-olds (image source: www.wildhorsepl.org/mustangs).

Mares most often foal for the first time as 3- or 4-year-olds and some older still, having become pregnant as 2-year-olds. Nevertheless, yearlings can also successfully conceive and foal as a 2-year-olds (image source: http://www.wildhorsepl.org/mustangs).

First-foaling as a 3-year-old was the norm

During the early years of the debate, however, high population growth rates were being calculated from sequences of population counts.

Counts from Beaty’s Butte and Jackie’s Butte during the 1970s indicated a 20-22% average annual increase [4].*

Similar, but probably less reliable count sequences, led to reports such as:

During the past 3 years it has been estimated that wild horse numbers are increasing at an estimated rate of 20-30% each year” [5] – C. Wayne Cook: Rangeman’s Journal, 1975

To achieve population growth of this magnitude, high foaling rates, especially by younger mares, were expected but not being supported by demographic evidence from the better studied populations.

From Assateague Islands and Chincoteague (1975-82) [1, 6], and the deserts of Wyoming (1978-79) [2] and Nevada (1980-82) [7], mares foaled for the first time only as 3-year-olds and most in all populations did not foal until they were 4 or 5 years old. Two-year-olds did not foal.

But then came Joel Berger’s landmark fieldwork in the Granite Range of Nevada during the early 1980s [8]. It changed our minds entirely.

Joel Berger's 1986 book - amongst the first to identify comparatively high reproductive rates amongst 2- and 3-year-old mares.

Joel Berger’s 1986 book – amongst the first to identify comparatively high reproductive rates amongst 2- and 3-year-old mares.

Teen pregnancy, Nevada

From 1979 to 1983 Joel Berger followed a population that was 58 at the beginning of his study.

He discovered extraordinary foaling rates, especially in younger mares foaling for the first time.

About 37% of 2-year-olds and 40% of 3-year-olds foaled. Given that 2-year-olds that foaled are unlikely to have foal again as 3-year-olds, these figures indicate that about 80% of mares foaled for the first time as 3-year-olds or younger. Suddenly, the capacity for rapid population growth was understood.

During the five years of the study, the Granite Range population grew by 91 horses to 149 – an instantaneous rate of increase (r) of 0.188 or a finite rate of increase (lambda, λ) of 1.21. In other words, the population had an average annual increase of 21% **. Clearly, two-year-old foaling in large numbers was possible.

Young mare foaling and eruptive growth

Joel’s work explains how some populations of horses can undergo, what is called, eruptive growth – short periods of maximum reproduction and survival leading to rapid population growth.

It is clear that for short periods of time, such as 4-5 years, extraordinarily high rates of first time foaling by 2- and 3-year-olds can translate into population growth that just exceeds 20% per annum. Importantly however, the population growth that Joel observed did not approach the earlier alarmist reports of growth rates up to up to 30% per annum [5].

Joel’s work linking first-time foaling rates and rapid population growth is exceptional and a useful insight into the largest growth rates possible for wild horse populations. Nevertheless, many subsequent studies would continue to demonstrate that in other places 2-year-old foaling was uncommon.

In similar North American studies on Pryor Mountain (1976-86) [9] and Cumberland Island (1986-90) [10], in the mountains of New Zealand (1994-98) [11], and grasslands of Argentina (1995-2002) [12], 2-year-old foaling either did not occur or was rare.

If 2-year-old foaling is possible and can occur at high rates, then why wasn’t it more commonly found?

Or, if 2-year-old foaling is more common than studies have detected, why is rapid population growth not more common?

– topics for subsequent posts.

Footnotes

* Eberhardt, Majorowicz & Wilcox (1982) has been repeatedly used as supporting evidence of high population growth rates in wild horse populations but the authors were careful to write “We do not propose that these herds are necessarily typical of feral horses in general”. It should not be assumed that the high growth rates reported by Eberhardt, Majorowicz & Wilcox are ubiquitous, only possible.

** In Joel Berger’s book (P76) the average finite rate of increase is written as 31%. This is incorrect and probably a printing error that should have read 21%. A 31% rate of increase would have generated 225 horses from 58 over the study period, not the 149 horses that were alive at the end of the study.

Bibliography

1. Keiper, R.R. (1979) Population dynamics of feral ponies. In Symposium on the ecology and behavior of feral and wild equids (Denniston, R.H., ed), pp. 175-183, University of Wyoming, Laramie.

2. Boyd, L. (1979) The mare-foal demography of feral horses in Wyoming’s Red Desert. In Symposium on the ecology and behavior of wild and feral equids (Denniston, R.H., ed), pp. 185-204, University of Wyoming, Laramie.

3. Seal, U.S. and Plotka, E.D. (1983) Age-specific pregnancy rates in feral horses. Journal of Wildlife Management 47, 422-429.

4. Eberhardt, L.L., et al. (1982) Apparent rates of increase for two feral horse herds. Journal of Wildlife Management 46, 367-374.

5. Cook, C.W. (1975) Wild horses and burros: a new management problem. Rangeman’s Journal 2, 19-21.

6. Keiper, R.R. and Houpt, K. (1984) Reproduction in feral horses: An eight year study. American Journal of Veterinary Research 45, 991-995.

7. Siniff, D., et al. (1982) Wild Horse Survival and Foaling Rates: Final Report to BLM (Contract AA851-CTO-52). University of Minnesota.

8. Berger, J. (1986) Wild horses of the Great Basin. University of Chicago Press.

9. Garrott, R. and Taylor, L. (1990) Dynamics of a feral horse population in Montana. Journal of Wildlife Management 54, 603-612.

10. Goodloe, R.B., et al. (2000) Population characteristics of feral horses on Cumberland Island, Goergia and their management implications. Journal of Wildlife Management 64, 114-121.

11. Linklater, W.L., et al. (2004) Feral horse demography and population growth in the Kaimanawa Ranges, New Zealand. Wildlife Research. 31, 119-128.

12. Scorolli, A.L. and Cazorla, A.C.L. (2010) Demography of feral horses (Equus caballus): a long-term study in Tornquist Park, Argentina. Wildlife Research 37, 207-214.

Ponies in Chincoteague National Wildlife Refuge (Image courtesy of TripAdvisor http://www.tripadvisor.com)

Chincoteague National Wildlife Refuge, during the late 1970s [1, 2], yielded an average 74% of mares foaling each year – the highest average rate ever reported.

The lowest average reproductive rate is reported from the Elcana Range, Nevada, from 1989 to 1998 when just 36% of mares foaled each year [3, 4].

All other populations have mare reproductive rates that fall between these two extremes. And so it is typical for around half of all mares of reproductive age to foal each year with some variation between populations (see the table below). Rates greater than 65% are comparatively high, and rates less than 50% are comparatively low.

No population is the same…

Large variation, therefore, exists between populations in reproductive rates and their capacity to grow. Most variation between populations is likely driven by the fundamental characters of their Table adult mare foalinglocations – their topography and climate – and the influence of those on the quantity and quality of food and shelter, and ease-of-access to water. Some places are just nicer and easier to live and breed.

… even from year to year

It is also evident from the accompanying table, however, that variation in annual reproductive rates from year to year for the same sites are greater than the spread of values between sites, due to annual changes in range conditions.

Range conditions can improve or deteriorate dramatically between years because they are driven by both changes in climate and animal density – food and shelter, and competition for them.

The high reproductive rates on Chinocoteague [1, 2], for example, were probably facilitated by the annual live harvest from the population that occurs to this day and reduces competition amongst horses for grazing.

The annual muster and swim of the Chincoteague ponies (image courtesy of The Baltimore Sun http://www.baltimoresun.com).

New Zealand’s wild horses in the Kaimanawa Mountains (highlighted in the Table) mares had comparatively moderate foaling rates averaging 55% during the late 1990s and so sit squarely between the extremes reported [5].  Nevertheless, the substantial population reductions that have occurred since this time are likely to have elevated reproductive rates.

It is likely that average, and especially single annual [6], rates could be found that are lower than the values shown – extreme climatic events or disease might result in some very poor foaling rates in some years. But it is much less likely that new higher values will be found. Individual annual rates exceeding 81% and average rates of around 75% are probably at or near the largest possible given the inherent constraints on mare reproduction.

These real-world values are a useful insight informing our conversation about population growth and what is and is not possible or claims credible.

The question of 2-year-olds foaling

In this post, I have considered only mares 3 years old and older as adult (reproductive age) because most studies, including those represented in the Table above, report that 2-year-olds did not foal. Nevertheless, in a few populations 2-year-olds do foal with potentially important consequences for population’s capacity to grow.

Does earlier-age  foaling elevate a population’s reproductive rate or are younger, still growing mares so exhausted by raising their foal that they are unable to foal again for several years?

I will address reproductive rates of 2-year-old and their adult mare populations next.

Bibliography and notes

1. Keiper RR. 1979. Population dynamics of feral ponies. In Symposium on the ecology and behavior of feral and wild equids; University of Wyoming, Laramie. Edited by Denniston RH. University of Wyoming, Laramie; 175-183.

2. Keiper R, Houpt K. 1984 Reproduction in feral horses: An eight year study. American Journal of Veterinary Research, 45:991-995.

3. Greger PD, Romney EM. 1999. High foal mortality limits growth of a desert feral horse population in Nevada. Great Basin Naturalist, 59:374-379.

4. I have not used values from studies where only one year of data is available because they are much less likely to represent the population average. For example, Kirkpatrick and Turner (1991) [6] reported 32.5% of mares foaling in 1990 on Assateague Island National Seashore.

5. Linklater WL, Cameron EZ, Minot EO, Stafford KJ. 2004. Feral horse demography and population growth in the Kaimanawa Ranges, New Zealand. Wildlife Research, 31:119-128.

6. Kirkpatrick JF, Turner JW. 1991. Compensatory reproduction in feral horses. Journal of Wildlife Management, 55:649-652.

7. Garrott R, Taylor L. 1990. Dynamics of a feral horse population in Montana. Journal of Wildlife Management, 54:603-612.

8. Scorolli AL, Cazorla ACL. 2010. Demography of feral horses (Equus caballus): a long-term study in Tornquist Park, Argentina. Wildlife Research, 37:207-214.

9. Goodloe RB, Warren RJ, Osborn DA, Hall C. 2000. Population characteristics of feral horses on Cumberland Island, Goergia and their management implications. Journal of Wildlife Management 2000, 64:114-121.

10. Boyd L. 1979. The mare-foal demography of feral horses in Wyoming’s Red Desert. In Symposium on the ecology and behavior of wild and feral equids; University of Wyoming, Laramie. Edited by Denniston RH. University of Wyoming, Laramie; 185-204.

The ratio of foals to other horses, or foals as a percentage of total population, are comparatively easy to gather and interpret reproductive rates that have a direct relationship to how much a population grows or declines each year (lambda, λ) and the population’s instantaneous rate of increase or decrease (r). Averaging and comparing reproductive rates over several years and how they vary from year to year provides insight about the potential of populations to grow.

Reproductive rates from Jackie’s and Beaty’s Buttes from 1969 to 1980 are amongst the highest and most variable reported. Around 26 foals for every 100 other horses was the average annual rate and it ranged from 15 to 39 foals for every 100 other horses in different years (image source: http://www.blm.gov).

The most extraordinary foaling rates with equally extraordinary variability between years are reported from Jackie’s Butte and Beaty’s Butte, Oregon. Foals to other horse ratios averaged 0.27 and 0.25, respectively, and ranged from 0.19 to 0.39 in Jackie’s Butte, and 0.22 to 0.30 in Beaty’s Butte, from 1969-80 [1]. Thus, foaling rates ranged up to 30% below to 44% above the 12-year average.Similarly high rates are reported from the Red Desert, Wyoming [2], where the foals to other horse ratios were 0.295 and 0.217 in 1978 and 1979, respectively (average 0.256).

Moderate foaling

Foaling rates were not nearly as high in other places but still highly variable from year to year. From 1990 to 1994, in the Elcana Range between the Mohave and Great Basin deserts, at a place better known for being Nevada’s nuclear weapons test site [3], foal to other horse ratios averaged 0.196 and ranged from 0.148 to 0.262, or from 25% below to 34% above the 5-year average [4]. In the Tornquist Park population, Argentina [5], the ratio is not presented but I was able to calculate it for 1995 and 2002 because population counts for those years are also given. Similarly, the foal to other horse ratio was 0.196 and 0.21 for those years.

…even though they had mare-biased sex ratios

Foaling rates on the Pryor Mountain Wild Horse Range from 1976 to 1986 averaged 0.189 and, although reported to be high [6], can be seen here to be moderate. Indeed, the reproductive rate was inflated by

Horses of the Assateague Island National Seashore (1975-79), like the Pryor Mountain herd around the same time, had twice as many mares as stallions but comparatively moderate reproductive rates less than 0.20 foals for every other horse, although a higher ratio of mares to stallions will elevate population-level reproductive rates (image source: tlc.howstuffworks.com).

an adult sex ratio biased towards mares. There were twice as many mares as stallions due to a history of removals that were selective of males. If managers had preserved an even ratio of adult mares and stallions the population would have reproduced itself at a much lower rate.

There were also over twice as many mares as stallions on the Assateague Island National Seashore (2.1 mares per stallion) when Ronald Keiper, Pennsylvania State University, investigated the population dynamics of its introduced horses during the late-1970s. Nevertheless, those rates too were moderate at 0.198 foals per other horse [7].

When comparing reproductive rates it is important to check for distortions in adult sex ratio away from male-female parity (that is equal in number). Stallion-biased sex ratios will suppress, and mare-biased ratios inflate, population-level reproductive rates like those presented here.

Lower foaling rates

Other places had much lower foaling rates. The foaling rate in Stone Cabin Valley, Nevada, during 1975 and 1976 was 0.12 and 0.18 foals for every other horse [8]. Similarly low rates of 0.15 to 0.19 between 1986 and 1990 also occurred on Cumberland Island, Georgia (USA) [9]. Examples of populations with lower reproductive rates appear to be less often written about although they must occur. One would expect a scientific publication bias towards populations with higher reprodcutuve rates where population impact and control, not conservation, has been the motivation for research.

More detailed demographic studies

Unfortunately, most other more detailed demographic studies are more difficult to interpret for comparison because they report the foaling rate as a percentage of adult mares foaling and define the age a mare is adult differently. Some define all females 3 years old and older as adult mares, while others consider 2-year-olds also adults.

This difference in how studies report foaling rate per adult female results because only a few populations report 2-year-olds foaling [10]. In most populations 2-year-olds were not reported to foal and so were excluded from calculations.

Joel Berger's 1986 book - amongst the first to identify comparatively high reproductive rates amongst 2- and 3-year-old mares.

Joel Berger’s 1986 book – amongst the first to identify comparatively high reproductive rates amongst 2- and 3-year-old mares.

Joel Berger reported 37% of 2-year-olds foaling in the Granite Range, Nevada [10], and was the first to find substantial foaling by young mares and so explain why some feral horse populations could grow more rapidly. Because the rate at which 2-year-olds foal may be critical to rapid population growth I will devote a post to two-year-old foaling rates later.

Upper limits to population growth

Studies report, therefore, from 15 to almost 30 foals per 100 other horses and so help define the upper limits of population growth. A population cannot grow 30% or more over several years if each year it averages fewer than 30 foals per 100 other horses each year.

For the moment, reports of the ratio of foals to other horses in populations indicate that their average growth rate should not exceed 27% per year and can vary considerably – by as much as 110%  between years and from 30% below to 44% above the long-term average.

Bibliography

1. Eberhardt, L.L., Majorowicz, A.K., Wilcox, J.A. 1982: Apparent rates of increase for two feral horse herds. Journal of Wildlife Management 1982, 46: 367-374.

2. Boyd, L. (1979) The mare-foal demography of feral horses in Wyoming’s Red Desert. In Symposium on the ecology and behavior of wild and feral equids (Denniston, R.H., ed), pp. 185-204, University of Wyoming, Laramie.

3. Nuclear explosions at Nevada’s nuclear weapons test site occurred above ground 1951 to July 62, and below ground until 1992.

4. Greger PD, Romney EM. 1999. High foal mortality limits growth of a desert feral horse population in Nevada. Great Basin Naturalist, 59:374-379.

5. Scorolli, A.L. and Cazorla, A.C.L. 2010. Demography of feral horses (Equus caballus): a long-term study in Tornquist Park, Argentina. Wildlife Research 37: 207-214.

6. Garrott R, Taylor L: Dynamics of a feral horse population in Montana. Journal of Wildlife Management 1990, 54:603-612.

7.Keiper RR: Population dynamics of feral ponies. In Symposium on the ecology and behavior of feral and wild equids; University of Wyoming, Laramie. Edited by Denniston RH. University of Wyoming, Laramie; 1979: 175-183.

8. Green, N.; Green, H. In The wild horse population of stone cabin valley, Nevada: A preliminary report, Proceedings of the National Wild Horse Forum, University of Nevada, Reno, 1977; University of Nevada, Reno, pp 59-65.

9. Goodloe, R.B.,Warren, R.J., Osborn, D.A., Hall, C. 2000. Population characteristics of feral horses on Cumberland Island, Goergia and their management implications. Journal of Wildlife Management 64, 114-121.

10. Berger, J. (1986) Wild horses of the Great Basin. University of Chicago Press.

The number of foals when compared to the number of other horses or total population is a useful measure of a population’s reproduction because it is so easily obtained and interpreted. It is also an indication of a population’s potential to grow because it cannot grow faster than it produces foals.

The ratio of foals to other horses, or percentage of foals in the population, is a powerful measure of reproduction because foals are easily distinguished from other horses during population estimates, it does not require that other horses be aged and sexed, and is an indication of the populations potential to grow. Photo source: http://www.reviewjournal.com.

Easy to get

Foals are quickly and reliably distinguished from other horses, even from a light plane or helicopter and especially if the population estimate is made soon after the end of the foaling season. Late-summer through early autumn would be the ideal time for most populations. Most foals are born late-spring and rarely in late-autumn and winter.

Importantly, the measurement does not require that other horses in the population are aged or sexed. More studies, even more detailed demographic studies, should present a ratio of foals to other horses to help make comparisons amongst populations.

Easy to interpret

Conveniently, the proportion of foals in the population (number of foals divided total population size) will be larger than a population’s instantaneous rate of increase – given the label r by population biologists – because there must also be deaths.

For the same reason, the ratio of foals to other horses (number of foals divided by the number of other horses) should be larger than a population’s growth in the same year – that is given the label lambda, λ.

A check for growth potential

Because the proportion of population that are foals and ratio Kaimanawa foaling rate text boxof foals to other horses should be larger than r and λ, respectively, they are a useful guide of a populations potential to grow or a useful retrospective check of the reliability of population growth estimates.

There are some egregious examples published in the scientific literature where extraordinary claims of feral horse population growth were larger than the foals in the population could support (see insert). When an estimate of population size is made, I recommend that a separate count of foals also be made to validate subsequent estimates of population growth.

 

Bibliography

1. Rogers, G.M. (1991) Kaimanawa feral horses and their environmental impacts. New Zealand Journal of Ecology 15, 49-64.

2. Linklater, W.L.,  Cameron, E.Z., Stafford, K.J., Minot, E.O. 2001. Estimating Kaimanawa feral horse population size and growth. Science & Research Unit, Science, Technology and Information Services, Department of Conservation.

3. Linklater, W.L.,Cameron, E.Z., Minot, E.O., Stafford, K.J. 2004. Feral horse demography and population growth in the Kaimanawa Ranges, New Zealand. Wildlife Research 31: 119-128.

For a population of wild horses to grow at an extraordinary rate:

I. a large proportion of mares, especially young mares, must reproduce each year,

II. only a small proportion of the population die each year, and

III. the variability in reproduction and survival between years must be small.

We have imagined a virtual population and conducted a series of simple calculations of its structure, reproduction, and death to understand the plausibility of extraordinary growth rates like 30% per year.

We discovered that growth rates like 30% are improbable over several years but might be possible in some years. However, our calculations assumed some extraordinary rates of reproduction and survival. In the real world, how realistic are such rates?

In a new series, under the category Demography – the study of the statistics of births and deaths – I will amass and compare all reports of horse reproduction and death. It is a large literature and the analysis will accumulate and develope as we delve into it.

I will begin with reproduction. You can’t grow a population without foals.

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